Subgroups — C₂×C₇×#2967 #13237415

Order 1792.

1970 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₇×#2967	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#446	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#436	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#435	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#435	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#433	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#405	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₇×C₈	C₂²	1	2	yes	—
14	C₇×#529	C₄	1	8	yes	—
15	C₇×#529	C₂²	1	8	yes	—
16	C₂×C₇×#126	C₄	1	2	yes	—
17	C₂×C₇×#125	C₄	1	1	yes	characteristic
18	C₂×C₇×#124	C₄	1	1	yes	characteristic
19	C₂×C₇×#123	C₄	1	2	yes	—
20	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
21	C₂×C₇×#121	C₄	1	1	yes	characteristic
22	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
25	C₂×C₇×#117	C₂²	1	2	yes	—
26	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
27	C₇×#446	C₂²	1	16	yes	complemented
28	C₇×#436	C₂²	1	16	yes	complemented
29	C₇×#435	C₂²	1	16	yes	complemented
30	C₇×#435	C₂²	1	16	yes	complemented
31	C₇×#433	C₂²	1	16	yes	complemented
32	C₇×#432	C₂²	1	8	yes	complemented
33	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
35	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
36	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
39	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
40	C₇×#405	C₂²	1	16	yes	complemented
41	C₄×C₇×M₁₆	C₂²	1	8	yes	complemented
42	C₂×C₇×#97	C₂²	1	2	yes	—
43	C₂×C₇×#97	C₂²	1	2	yes	—
44	C₂×C₇×#97	C₂²	1	2	yes	—
45	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
47	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
48	C₂×#2967	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
51	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₇	C₂³	1	2	yes	—
56	C₂×C₇×M₁₆	—	2	8	no	—
57	C₂×C₇×M₁₆	—	2	8	no	—
58	C₂×C₇×M₁₆	C₂³	1	8	yes	—
59	C₂×C₇×M₁₆	C₂³	1	8	yes	—
60	C₂²×C₇×C₈	—	2	8	no	—
61	C₂²×C₇×C₈	C₂³	1	8	yes	—
62	C₂²×C₇×C₈	C₂³	1	2	yes	—
63	C₂²×C₇×C₈	C₂³	1	2	yes	—
64	C₂²×C₇×C₈	C₂³	1	2	yes	—
65	C₂²×C₇×C₈	C₂³	1	2	yes	—
66	C₇×#126	C₂×C₄	1	16	yes	—
67	C₇×#125	C₂×C₄	1	8	yes	—
68	C₇×#124	C₂×C₄	1	8	yes	—
69	C₇×#123	C₂×C₄	1	16	yes	—
70	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
71	C₇×#121	C₂×C₄	1	8	yes	—
72	C₄×C₇×Q₈	C₂×C₄	1	4	yes	—
73	C₄×C₇×Q₈	C₂³	1	4	yes	—
74	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
75	C₄×C₇×D₄	C₂×C₄	1	8	yes	—
76	C₄×C₇×D₄	C₂³	1	4	yes	—
77	C₄×C₇×D₄	C₂³	1	8	yes	—
78	C₇×#117	C₂×C₄	1	8	yes	—
79	C₇×#117	C₂³	1	8	yes	—
80	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
81	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
82	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
84	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
86	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
87	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
88	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
89	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
90	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₇	C₂×C₄	1	4	yes	—
94	C₂×C₄²×C₇	C₂³	1	4	yes	—
95	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇	C₂³	1	2	yes	—
98	C₇×C₄⋊C₈	C₂³	1	8	yes	—
99	C₇×C₄⋊C₈	C₂³	1	8	yes	—
100	C₇×C₄⋊C₈	C₂³	1	8	yes	—
101	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
102	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
103	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
104	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
105	C₇×#97	C₂³	1	8	yes	—
106	C₇×#97	C₂³	1	8	yes	—
107	C₇×#97	C₂³	1	8	yes	—
108	C₄×C₇×C₈	C₂³	1	4	yes	—
109	C₄×C₇×C₈	C₂³	1	4	yes	—
110	C₄×C₇×C₈	C₂³	1	8	yes	—
111	C₂×#529	C₂×C₇	1	1	yes	characteristic
112	#2967	C₂×C₇	1	16	yes	direct product factor
113	C₂×#446	C₂×C₇	1	2	yes	complemented
114	C₂×#436	C₂×C₇	1	2	yes	complemented
115	C₂×#435	C₂×C₇	1	2	yes	complemented
116	C₂×#435	C₂×C₇	1	2	yes	complemented
117	C₂×#433	C₂×C₇	1	2	yes	complemented
118	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
119	C₂×#405	C₂×C₇	1	2	yes	complemented
120	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
121	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
122	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₇×Q₈	—	4	2	no	—
124	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
125	C₂×C₇×D₄	—	4	2	no	—
126	C₂×C₇×D₄	—	4	4	no	—
127	C₂×C₇×D₄	C₂²×C₄	1	8	yes	—
128	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₇	—	2	4	no	—
130	C₂²×C₄×C₇	—	2	4	no	—
131	C₂²×C₄×C₇	—	2	4	no	—
132	C₂²×C₄×C₇	—	4	2	no	—
133	C₂²×C₄×C₇	—	4	2	no	—
134	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
146	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
149	C₇×M₁₆	—	2	16	no	—
150	C₇×M₁₆	—	2	16	no	—
151	C₂×C₇×C₈	—	2	4	no	—
152	C₂×C₇×C₈	—	2	4	no	—
153	C₂×C₇×C₈	—	2	4	no	—
154	C₂×C₇×C₈	—	2	16	no	—
155	C₂×C₇×C₈	#41	1	8	yes	—
156	C₂×C₇×C₈	C₂⁴	1	4	yes	—
157	C₂×C₇×C₈	C₂⁴	1	4	yes	—
158	C₂×C₇×C₈	C₂⁴	1	4	yes	—
159	C₂×C₇×C₈	C₂⁴	1	4	yes	—
160	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
161	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
162	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
163	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
164	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
165	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
166	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
167	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
168	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
169	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
170	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
171	C₄²×C₇	C₂²×C₄	1	2	yes	—
172	C₄²×C₇	C₂²×C₄	1	2	yes	—
173	C₄²×C₇	C₂²×C₄	1	4	yes	—
174	C₄²×C₇	C₂²×C₄	1	4	yes	—
175	C₄²×C₇	C₂²×C₄	1	4	yes	—
176	C₄²×C₇	C₂⁴	1	2	yes	—
177	C₄²×C₇	C₂⁴	1	4	yes	—
178	C₄²×C₇	C₂⁴	1	2	yes	—
179	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
180	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
181	C₂³×C₈	C₂²×C₇	1	2	yes	—
182	#529	C₄×C₇	1	8	yes	—
183	#529	C₂²×C₇	1	8	yes	—
184	C₂×#126	C₄×C₇	1	2	yes	—
185	C₂×#125	C₄×C₇	1	1	yes	characteristic
186	C₂×#124	C₄×C₇	1	1	yes	characteristic
187	C₂×#123	C₄×C₇	1	2	yes	—
188	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
189	C₂×#121	C₄×C₇	1	1	yes	characteristic
190	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
191	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
192	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
193	C₂×#117	C₂²×C₇	1	2	yes	—
194	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
195	#446	C₂²×C₇	1	16	yes	complemented
196	#436	C₂²×C₇	1	16	yes	complemented
197	#435	C₂²×C₇	1	16	yes	complemented
198	#435	C₂²×C₇	1	16	yes	complemented
199	#433	C₂²×C₇	1	16	yes	complemented
200	#432	C₂²×C₇	1	8	yes	complemented
201	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
204	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
205	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
206	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
207	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
208	#405	C₂²×C₇	1	16	yes	complemented
209	C₄×M₁₆	C₂²×C₇	1	8	yes	complemented
210	C₂×#97	C₂²×C₇	1	2	yes	—
211	C₂×#97	C₂²×C₇	1	2	yes	—
212	C₂×#97	C₂²×C₇	1	2	yes	—
213	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
215	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
216	C₂³×C₇	—	2	4	no	—
217	C₂³×C₇	—	2	2	no	—
218	C₂³×C₇	—	2	2	no	—
219	C₂³×C₇	—	2	2	no	—
220	C₂³×C₇	—	2	4	no	—
221	C₂³×C₇	—	2	4	no	—
222	C₂³×C₇	C₂³×C₄	1	4	yes	—
223	C₂³×C₇	C₂³×C₄	1	2	yes	—
224	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
225	C₇×Q₈	—	4	4	no	—
226	C₇×D₄	—	4	4	no	—
227	C₇×D₄	—	4	8	no	—
228	C₂×C₄×C₇	—	2	4	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	2	no	—
234	C₂×C₄×C₇	—	2	4	no	—
235	C₂×C₄×C₇	—	2	4	no	—
236	C₂×C₄×C₇	—	2	8	no	—
237	C₂×C₄×C₇	—	2	4	no	—
238	C₂×C₄×C₇	—	2	4	no	—
239	C₂×C₄×C₇	—	2	4	no	—
240	C₂×C₄×C₇	—	2	4	no	—
241	C₂×C₄×C₇	—	4	4	no	—
242	C₂×C₄×C₇	—	4	4	no	—
243	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
244	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
245	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
246	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
247	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
248	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
249	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
250	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
251	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₇	C₂×#41	1	4	yes	—
253	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
254	C₇×C₈	—	2	4	no	—
255	C₇×C₈	—	2	4	no	—
256	C₇×C₈	—	2	4	no	—
257	C₇×C₈	C₂×#41	1	8	yes	—
258	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
259	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
260	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
261	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
262	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₇	1	2	yes	—
264	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
265	C₂×M₁₆	—	2	8	no	—
266	C₂×M₁₆	—	2	8	no	—
267	C₂×M₁₆	C₂³×C₇	1	8	yes	—
268	C₂×M₁₆	C₂³×C₇	1	8	yes	—
269	C₂²×C₈	—	2	8	no	—
270	C₂²×C₈	C₂³×C₇	1	2	yes	—
271	C₂²×C₈	C₂³×C₇	1	8	yes	—
272	C₂²×C₈	C₂³×C₇	1	2	yes	—
273	C₂²×C₈	C₂³×C₇	1	2	yes	—
274	C₂²×C₈	C₂³×C₇	1	2	yes	—
275	#126	C₂×C₄×C₇	1	16	yes	—
276	#125	C₂×C₄×C₇	1	8	yes	—
277	#124	C₂×C₄×C₇	1	8	yes	—
278	#123	C₂×C₄×C₇	1	16	yes	—
279	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
280	#121	C₂×C₄×C₇	1	8	yes	—
281	C₄×Q₈	C₂×C₄×C₇	1	4	yes	—
282	C₄×Q₈	C₂³×C₇	1	4	yes	—
283	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
284	C₄×D₄	C₂×C₄×C₇	1	8	yes	—
285	C₄×D₄	C₂³×C₇	1	4	yes	—
286	C₄×D₄	C₂³×C₇	1	8	yes	—
287	#117	C₂×C₄×C₇	1	8	yes	—
288	#117	C₂³×C₇	1	8	yes	—
289	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
290	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
291	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
293	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
295	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
297	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
300	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
301	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
302	C₂×C₄²	C₂×C₄×C₇	1	4	yes	—
303	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₇	1	2	yes	—
305	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
306	C₂×C₄²	C₂³×C₇	1	4	yes	—
307	C₄⋊C₈	C₂³×C₇	1	8	yes	—
308	C₄⋊C₈	C₂³×C₇	1	8	yes	—
309	C₄⋊C₈	C₂³×C₇	1	8	yes	—
310	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
311	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
312	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
313	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
314	#97	C₂³×C₇	1	8	yes	—
315	#97	C₂³×C₇	1	8	yes	—
316	#97	C₂³×C₇	1	8	yes	—
317	C₄×C₈	C₂³×C₇	1	4	yes	—
318	C₄×C₈	C₂³×C₇	1	4	yes	—
319	C₄×C₈	C₂³×C₇	1	8	yes	—
320	C₂²×C₇	—	2	4	no	—
321	C₂²×C₇	—	2	2	no	—
322	C₂²×C₇	—	2	2	no	—
323	C₂²×C₇	—	2	2	no	—
324	C₂²×C₇	—	2	4	no	—
325	C₂²×C₇	—	2	4	no	—
326	C₂²×C₇	—	4	4	no	—
327	C₂²×C₇	—	4	8	no	—
328	C₂²×C₇	C₄×#41	1	2	yes	—
329	C₂²×C₇	#568	1	2	yes	—
330	C₂²×C₇	#568	1	2	yes	—
331	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
332	C₄×C₇	—	2	4	no	—
333	C₄×C₇	—	2	2	no	—
334	C₄×C₇	—	2	2	no	—
335	C₄×C₇	—	2	2	no	—
336	C₄×C₇	—	2	2	no	—
337	C₄×C₇	—	2	2	no	—
338	C₄×C₇	—	2	4	no	—
339	C₄×C₇	—	2	4	no	—
340	C₄×C₇	C₄×#41	1	2	yes	—
341	C₄×C₇	C₂²×#41	1	2	yes	—
342	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
343	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	4	no	—
348	C₂×D₄	C₂²×C₄×C₇	1	8	yes	—
349	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
356	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
363	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
364	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
365	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
366	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
370	M₁₆	—	2	16	no	—
371	M₁₆	—	2	16	no	—
372	C₂×C₈	—	2	4	no	—
373	C₂×C₈	—	2	4	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	2	16	no	—
376	C₂×C₈	C₇×#41	1	8	yes	—
377	C₂×C₈	C₂⁴×C₇	1	4	yes	—
378	C₂×C₈	C₂⁴×C₇	1	4	yes	—
379	C₂×C₈	C₂⁴×C₇	1	4	yes	—
380	C₂×C₈	C₂⁴×C₇	1	4	yes	—
381	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
382	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
383	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
384	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
385	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
386	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
387	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
388	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
389	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
390	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
391	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
392	C₄²	C₂²×C₄×C₇	1	2	yes	—
393	C₄²	C₂²×C₄×C₇	1	2	yes	—
394	C₄²	C₂²×C₄×C₇	1	4	yes	—
395	C₄²	C₂²×C₄×C₇	1	4	yes	—
396	C₄²	C₂²×C₄×C₇	1	4	yes	—
397	C₄²	C₂⁴×C₇	1	2	yes	—
398	C₄²	C₂⁴×C₇	1	4	yes	—
399	C₄²	C₂⁴×C₇	1	2	yes	—
400	C₂×C₇	—	4	2	no	—
401	C₂×C₇	—	4	4	no	—
402	C₂×C₇	#2967	1	4	yes	direct product factor
403	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
404	C₂×C₇	C₂×#568	1	1	yes	characteristic
405	C₂×C₇	C₂×#568	1	1	yes	characteristic
406	C₂³	—	2	4	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	4	no	—
412	C₂³	C₂³×C₄×C₇	1	4	yes	—
413	C₂³	C₂³×C₄×C₇	1	2	yes	—
414	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
415	Q₈	—	4	4	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
434	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
435	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
436	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
437	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
438	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
439	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
440	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
441	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
442	C₂×C₄	C₂×C₇×#41	1	4	yes	—
443	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
444	C₈	—	2	4	no	—
445	C₈	—	2	4	no	—
446	C₈	—	2	4	no	—
447	C₈	C₂×C₇×#41	1	8	yes	—
448	C₇	C₂×#2967	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	8	no	—
457	C₂²	C₄×C₇×#41	1	2	yes	—
458	C₂²	C₇×#568	1	2	yes	—
459	C₂²	C₇×#568	1	2	yes	—
460	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	4	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	4	no	—
468	C₄	—	2	2	no	—
469	C₄	C₄×C₇×#41	1	2	yes	—
470	C₄	C₂²×C₇×#41	1	2	yes	—
471	C₂	—	4	2	no	—
472	C₂	—	4	4	no	—
473	C₂	C₇×#2967	1	4	yes	direct product factor
474	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
475	C₂	C₂×C₇×#568	1	1	yes	characteristic
476	C₂	C₂×C₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂³×C₇	C₂³×C₄
prime radical	C₂×C₇×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₇×#2967	C₂	direct (N × H)
3. C₂×C₇×#446	C₂	semidirect
4. C₂×C₇×#436	C₂	semidirect
5. C₂×C₇×#435	C₂	semidirect
6. C₂×C₇×#435	C₂	semidirect
7. C₂×C₇×#433	C₂	semidirect
8. C₂×C₇×#432	C₂	semidirect
9. C₂×C₇×#405	C₂	semidirect
10. C₂×C₄×C₇×M₁₆	C₂	semidirect
27. C₇×#446	C₂²	semidirect
28. C₇×#436	C₂²	semidirect
29. C₇×#435	C₂²	semidirect
30. C₇×#435	C₂²	semidirect
31. C₇×#433	C₂²	semidirect
32. C₇×#432	C₂²	semidirect
40. C₇×#405	C₂²	semidirect
41. C₄×C₇×M₁₆	C₂²	semidirect
48. C₂×#2967	C₇	direct (N × H)
112. #2967	C₂×C₇	direct (N × H)
113. C₂×#446	C₂×C₇	semidirect
114. C₂×#436	C₂×C₇	semidirect
115. C₂×#435	C₂×C₇	semidirect
116. C₂×#435	C₂×C₇	semidirect
117. C₂×#433	C₂×C₇	semidirect
118. C₂×#432	C₂×C₇	semidirect
119. C₂×#405	C₂×C₇	semidirect
120. C₂×C₄×M₁₆	C₂×C₇	semidirect
195. #446	C₂²×C₇	semidirect
196. #436	C₂²×C₇	semidirect
197. #435	C₂²×C₇	semidirect
198. #435	C₂²×C₇	semidirect
199. #433	C₂²×C₇	semidirect
200. #432	C₂²×C₇	semidirect
208. #405	C₂²×C₇	semidirect
209. C₄×M₁₆	C₂²×C₇	semidirect
402. C₂×C₇	#2967	direct (N × H)
448. C₇	C₂×#2967	direct (N × H)
473. C₂	C₇×#2967	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#529	2
C₇×#2967	2
C₂×C₇×#446	2
C₂×C₇×#436	2
C₂×C₇×#435	2
C₂×C₇×#433	2
C₂×C₇×#432	2
C₂×C₇×#405	2
C₂×C₄×C₇×M₁₆	2
C₂×#2967	7

Subgroups — C2×C7×#2967 #13237415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2967 #13237415